Search results for "NULL"
showing 10 items of 396 documents
Extending conventional priors for testing general hypotheses in linear models
2007
We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalizat…
A weighted combined effect measure for the analysis of a composite time-to-first-event endpoint with components of different clinical relevance
2018
Composite endpoints combine several events within a single variable, which increases the number of expected events and is thereby meant to increase the power. However, the interpretation of results can be difficult as the observed effect for the composite does not necessarily reflect the effects for the components, which may be of different magnitude or even point in adverse directions. Moreover, in clinical applications, the event types are often of different clinical relevance, which also complicates the interpretation of the composite effect. The common effect measure for composite endpoints is the all-cause hazard ratio, which gives equal weight to all events irrespective of their type …
PValues for Composite Null Models
2000
Abstract The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial…
Analisis bayesiano de los contrastes de hipotesis parametricos
1985
Classical solutions to parametric hypothesis testing are shown to be particular instances of the Bayesian solution to a decision problem with two alternatives, in which the increase in utility for rejecting a false null is a linear function of the discrepancy between the accepted parametric model and the more likely model under the null.
A critical evaluation of the current “p-value controversy”
2017
This article has been triggered by the initiative launched in March 2016 by the Board of Directors of the American Statistical Association (ASA) to counteract the current p-value focus of statistical research practices that allegedly "have contributed to a reproducibility crisis in science." It is pointed out that in the very wide field of statistics applied to medicine, many of the problems raised in the ASA statement are not as severe as in the areas the authors may have primarily in mind, although several of them are well-known experts in biostatistics and epidemiology. This is mainly due to the fact that a large proportion of medical research falls under the realm of a well developed bo…
On delocalization of eigenvectors of random non-Hermitian matrices
2019
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-\log^{2} n}$ $$ \min\limits_{I\subset[n],\,|I|= m}\|{\bf v}_I\| \geq \frac{m^{3/2}}{n^{3/2}\log^Cn}\|{\bf v}\| $$ for any real eigenvector ${\bf v}$ and any $m\in[\log^C n,n]$, where ${\bf v}_I$ denotes the restriction of ${\bf v}$ to $I$. Further, when the entries of $A$ are complex, with i.i.d real and imaginary parts, we show that with probability at least $1-e^{-\log^{2} n}$ all eigenvectors of $A$ are delocalized in the sense that $$ \min\l…
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Residuenanalyse des Unabhängigkeitsmodells Zweier Kategorialer Variablen
1985
For the ‘cellwise’ analysis of independence of two categorial variables, Haberman (1973) proposes the method of ‘adjusted residuals’. Fuchs and Kenett (1980) use (the absolute value of) the maximal adjusted residual as a measure for the deviation from the null hypothesis.
THE ROLE OF UNBOUNDED TIME-SCALES IN GENERATING LONG-RANGE MEMORY IN ADDITIVE MARKOVIAN PROCESSES
2013
Any additive stationary and continuous Markovian process described by a Fokker–Planck equation can also be described in terms of a Schrödinger equation with an appropriate quantum potential. By using such analogy, it has been proved that a power-law correlated stationary Markovian process can stem from a quantum potential that (i) shows an x-2 decay for large x values and (ii) whose eigenvalue spectrum admits a null eigenvalue and a continuum part of positive eigenvalues attached to it. In this paper we show that such two features are both necessary. Specifically, we show that a potential with tails decaying like x-μ with μ < 2 gives rise to a stationary Markovian process which is not p…
Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points
2021
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…